Chapter 1.6, Problem 91E

(a)

To determine

To graph: The function, $f\left(x\right)=\cot x$, and determine the behaviour of the function as $x\to 0^{+}$ such that $x\to c^{+}$ indicates that $x$ approaches $c$ from the right and $x\to c^{-}$ indicates that $x$ approaches $c$ from the left.

(b)

To determine

To graph: The function, $f\left(x\right)=\cot x$, and determine the behaviour of the function as $x\to 0^{-}$ such that $x\to c^{+}$ indicates that $x$ approaches $c$ from the right and $x\to c^{-}$ indicates that $x$ approaches $c$ from the left.

(c)

To determine

To graph: The function, $f\left(x\right)=\cot x$, and determine the behaviour of the function as $x\to {\pi }^{+}$ such that $x\to c^{+}$ indicates that $x$ approaches $c$ from the right and $x\to c^{-}$ indicates that $x$ approaches $c$ from the left.

(d)

To determine

To graph: The function, $f\left(x\right)=\cot x$, and determine the behaviour of the function as $x\to {\pi }^{-}$ such that $x\to c^{+}$ indicates that $x$ approaches $c$ from the right and $x\to c^{-}$ indicates that $x$ approaches $c$ from the left.